Quotes About Calculus

Calculus succeeds by breaking complicated problems down into simpler parts. That strategy, of course, is not unique to calculus. All good problem-solvers know that hard problems become easier when they're split into chunks. The truly radical and distinctive move of calculus is that it takes this divide-and-conquer strategy to its utmost extreme — all the way out to infinity.

Nature—cue the theme from The Twilight Zone—somehow knows calculus.

Literalism is like giving a child a calculus book as a step stool to reach a washbasin. In so doing, much is lost that lies with the proper use of the book. Certainly children need step stools, but that particular use misses the true potential the book has to offer.

Yet in another way, calculus is fundamentally naive, almost childish in its optimism. Experience teaches us that change can be sudden, discontinuous, and wrenching. Calculus draws its power by refusing to see that. It insists on a world without accidents, where one thing leads logically to another. Give me the initial conditions and the law of motion, and with calculus I can predict the future -- or better yet, reconstruct the past. I wish I could do that now.

Voltaire called the calculus "the Art of numbering and measuring exactly a Thing whose Existence cannot be conceived." See Letters Concerning the English Nation p. 152

In making the basis of the calculus more rigorously formal, Weierstrass also attacked the appeal to intuition of continuous motion which is implied in Cauchy's expression -- that a variable approaches a limit.

Newton had considered the calculus as a scientific description of the generation of magnitudes, and Leibniz had viewed it as a metaphysical explanation of such generation. The formalism of the nineteenth century took from the calculus any such preconceptions, leaving only the bare symbolic relationships between abstract mathematical entities.

As the sensations of motion and discreteness led to the abstract notions of the calculus, so may sensory experience continue thus to suggest problem for the mathematician, and so may she in turn be free to reduce these to the basic formal logical relationships involved. Thus only may be fully appreciated the twofold aspect of mathematics: as the language of a descriptive interpretation of the relationships discovered in natural phenomena, and as a syllogistic elaboration of arbitrary premise.

Berkeley explained that by finding the tangent by means of differentials, one first assumes increments; but these determine the secant, not the tangent. One undoes this error, however, by neglecting higher differentials, and thus "by virtue of a twofold mistake you arrive, though not at science, yet at the truth.

Most of his predecessors had considered the differential calculus as bound up with geometry, but Euler made the subject a formal theory of functions which had no need to revert to diagrams or geometrical conceptions.

I turn aside with a shudder of horror from this lamentable plague of functions which have no derivatives.

a mathematician could show how a triangle's angles sum to 180 degrees, or any other geometric fact. On the other hand, calculus was based on faith.

I have always had an uncomfortable relationship with math. I don't like numbers for the sake of numbers. I am not impressed by fancy formulas that have no real-world application. I particularly disliked high school calculus for the simple reason that no one ever bothered to tell me why I needed to learn it. What is the area beneath a parabola? Who cares?

The emptiness of mere majority calculus deprives legality of all persuasive power.

In his eighteenth-century system of the world, Newton brought together two themes. Embodied in his calculus and physics, one Newtonian revelation rendered the physical world predictable and measurable. Another, less celebrated, was his key role in establishing a trustworthy gold standard, which made economic valuations as calculable and reliable as the physical dimensions of items in trade.

To the degree that we can demonstrate support for the Ukrainian government, we can change Putin's calculus and increase the risk to him and to Russia for moving combat forces closer to Kiev.

Aerodynamics is mathematics for those who haven't learned to do calculus. In my case, too, for one who hasn't learned to add or multiply, at least the first time.

magic was ugly—-a hard bargain with the universe, a calculus of pain.

By applying the same optical principles responsible for normal eyesight it was possible to extend vision artificially; similarly, the calculus of probabilities formalized the good sense that came naturally to the fortunate few to help out the befuddled many.

For every moment of triumph, there is an unequal and opposite feeling of despair. Take that iconic photograph of Muhammad Ali standing triumphantly over the prostrate, semiconscious wreckage of Sonny Liston. Great photo. Now think of Liston. Do the pleasure/pain calculus.

With an absurd oversimplification, the "invention" of calculus [method in mathematics] is sometimes ascribed to two men, Newton and Leibniz.

In politics you couldn't please everybody, but you still had to do the calculus to please most of everybody, or you didn't get the votes.

From my point of view, any outstanding work of art is a fantasy insofar as it reflects the unique world of a unique individual. Art is not just simple arithmetic, it's a delicate calculus. Keep in mind the passion of the scientist and the precision of the artist.

Math is radical!